The structure of linear relations in Euclidean spaces Original Research Article

The structure of a linear relation (multivalued operator) in a Euclidean space is completely determined. A linear relation can be written as a direct sum of three relations of different classes, which are Jordan relations, completely singular relations and multishifts. All three classes of relations are characterized in terms of the spectrum and their chain structure, which leads to a generalization of the classical Jordan canonical form.